Equivalent latent model will be, \[ \begin{bmatrix} \mathbf{w} \\ \mathbf{z} \end{bmatrix} \sim \mathbf{N}\left( \begin{bmatrix} \boldsymbol{\mu}_{w} \\ \boldsymbol{\mu}_x \end{bmatrix}, \begin{bmatrix} \boldsymbol{\Sigma}_{ww} & \boldsymbol{\Sigma}_{wz} \\ \boldsymbol{\Sigma}_{zw} & \boldsymbol{\Sigma}_{zz} \end{bmatrix} \right) \]
How much should I discuss about simrel-M??
n): 100m): 4relpos): 1, 2, 3, 4ypos): 1, 2, 3, 4p): 2 levels (20, 250)gamma): 2 levels (0.2, 0.9)eta): 2 levels (0, 0.4, 0.8, 1.2)R2: 2 levels (0.8; 0.4)Covariance structure of first design is,
Methods used in the study and their short description (how they estimate, what are they based on)
As Xenv, Yenv and Senv are based on maximum likelihood estimation, principal components of predictors explaining 99.5% of their variation are used.
In the model the prediction error for each of three response variables are used as response variable and following variables (with levels) and their complete interactions are used as predictor variables.
Following is the MANOVA output for estimation error and prediction error models using number of components (tuning parameters) that results minimum error.
Estimation Error Model:
Analysis of Variance Table
Df Pillai approx F num Df den Df Pr(>F)
(Intercept) 1 0.73310 7535.0 4 10973 < 2.2e-16 ***
p 1 0.04149 118.7 4 10973 < 2.2e-16 ***
gamma 1 0.52520 3034.4 4 10973 < 2.2e-16 ***
eta 3 0.03545 32.8 12 32925 < 2.2e-16 ***
R2 1 0.05762 167.7 4 10973 < 2.2e-16 ***
Method 6 0.72237 403.2 24 43904 < 2.2e-16 ***
p:gamma 1 0.00871 24.1 4 10973 < 2.2e-16 ***
p:eta 3 0.00192 1.8 12 32925 0.0490926 *
gamma:eta 3 0.00925 8.5 12 32925 2.631e-16 ***
p:R2 1 0.00772 21.4 4 10973 < 2.2e-16 ***
gamma:R2 1 0.03540 100.7 4 10973 < 2.2e-16 ***
eta:R2 3 0.00145 1.3 12 32925 0.1937604
p:Method 6 0.11772 55.5 24 43904 < 2.2e-16 ***
gamma:Method 6 0.58455 313.1 24 43904 < 2.2e-16 ***
eta:Method 18 0.01487 2.3 72 43904 4.387e-09 ***
R2:Method 6 0.27841 136.9 24 43904 < 2.2e-16 ***
p:gamma:eta 3 0.00122 1.1 12 32925 0.3404456
p:gamma:R2 1 0.00163 4.5 4 10973 0.0013196 **
p:eta:R2 3 0.00109 1.0 12 32925 0.4445299
gamma:eta:R2 3 0.00089 0.8 12 32925 0.6332008
p:gamma:Method 6 0.02259 10.4 24 43904 < 2.2e-16 ***
p:eta:Method 18 0.00988 1.5 72 43904 0.0033841 **
gamma:eta:Method 18 0.01067 1.6 72 43904 0.0005951 ***
p:R2:Method 6 0.02578 11.9 24 43904 < 2.2e-16 ***
gamma:R2:Method 6 0.18226 87.3 24 43904 < 2.2e-16 ***
eta:R2:Method 18 0.00791 1.2 72 43904 0.1100396
p:gamma:eta:R2 3 0.00138 1.3 12 32925 0.2337892
p:gamma:eta:Method 18 0.00785 1.2 72 43904 0.1199665
p:gamma:R2:Method 6 0.00553 2.5 24 43904 4.908e-05 ***
p:eta:R2:Method 18 0.00723 1.1 72 43904 0.2551289
gamma:eta:R2:Method 18 0.00610 0.9 72 43904 0.6419794
p:gamma:eta:R2:Method 18 0.00757 1.2 72 43904 0.1709646
Residuals 10976
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Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Prediction Error Model:
Analysis of Variance Table
Df Pillai approx F num Df den Df Pr(>F)
(Intercept) 1 0.99979 13042636 4 10973 < 2.2e-16 ***
p 1 0.00031 1 4 10973 0.488646
gamma 1 0.10168 311 4 10973 < 2.2e-16 ***
eta 3 1.00003 1372 12 32925 < 2.2e-16 ***
R2 1 0.98330 161522 4 10973 < 2.2e-16 ***
Method 6 0.20035 96 24 43904 < 2.2e-16 ***
p:gamma 1 0.00019 1 4 10973 0.713312
p:eta 3 0.00112 1 12 32925 0.420803
gamma:eta 3 0.00448 4 12 32925 1.937e-06 ***
p:R2 1 0.00036 1 4 10973 0.410451
gamma:R2 1 0.00107 3 4 10973 0.018992 *
eta:R2 3 0.00810 7 12 32925 7.492e-14 ***
p:Method 6 0.00460 2 24 43904 0.001231 **
gamma:Method 6 0.09142 43 24 43904 < 2.2e-16 ***
eta:Method 18 0.07152 11 72 43904 < 2.2e-16 ***
R2:Method 6 0.04785 22 24 43904 < 2.2e-16 ***
p:gamma:eta 3 0.00143 1 12 32925 0.207494
p:gamma:R2 1 0.00120 3 4 10973 0.010454 *
p:eta:R2 3 0.00174 2 12 32925 0.087104 .
gamma:eta:R2 3 0.00127 1 12 32925 0.303652
p:gamma:Method 6 0.00275 1 24 43904 0.178302
p:eta:Method 18 0.00857 1 72 43904 0.040237 *
gamma:eta:Method 18 0.02426 4 72 43904 < 2.2e-16 ***
p:R2:Method 6 0.00313 1 24 43904 0.079073 .
gamma:R2:Method 6 0.00283 1 24 43904 0.150836
eta:R2:Method 18 0.01680 3 72 43904 7.002e-12 ***
p:gamma:eta:R2 3 0.00248 2 12 32925 0.007171 **
p:gamma:eta:Method 18 0.00356 1 72 43904 0.999463
p:gamma:R2:Method 6 0.00196 1 24 43904 0.605334
p:eta:R2:Method 18 0.00716 1 72 43904 0.275495
gamma:eta:R2:Method 18 0.00555 1 72 43904 0.817756
p:gamma:eta:R2:Method 18 0.00645 1 72 43904 0.512952
Residuals 10976
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Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Study of Effect